Vice President Joe Biden on Tuesday urged Kurdistan's top official to work closely with Iraq's prime minister-designate as he tries to form a government, underscoring the U.S. push for a new and more inclusive leadership in the troubled nation.

The call also reinforced U.S. efforts to integrate the Kurdish leadership into the evolving governance structure in Baghdad, while the U.S. has begun covertly to provide arms directly to the Kurds, in consultation with the central Iraqi government, to help them fight the militants...